/*
 * Copyright (c) 2009-2010 Apple Inc. All rights reserved.
 *
 * @APPLE_OSREFERENCE_LICENSE_HEADER_START@
 *
 * This file contains Original Code and/or Modifications of Original Code
 * as defined in and that are subject to the Apple Public Source License
 * Version 2.0 (the 'License'). You may not use this file except in
 * compliance with the License. The rights granted to you under the License
 * may not be used to create, or enable the creation or redistribution of,
 * unlawful or unlicensed copies of an Apple operating system, or to
 * circumvent, violate, or enable the circumvention or violation of, any
 * terms of an Apple operating system software license agreement.
 *
 * Please obtain a copy of the License at
 * http://www.opensource.apple.com/apsl/ and read it before using this file.
 *
 * The Original Code and all software distributed under the License are
 * distributed on an 'AS IS' basis, WITHOUT WARRANTY OF ANY KIND, EITHER
 * EXPRESS OR IMPLIED, AND APPLE HEREBY DISCLAIMS ALL SUCH WARRANTIES,
 * INCLUDING WITHOUT LIMITATION, ANY WARRANTIES OF MERCHANTABILITY,
 * FITNESS FOR A PARTICULAR PURPOSE, QUIET ENJOYMENT OR NON-INFRINGEMENT.
 * Please see the License for the specific language governing rights and
 * limitations under the License.
 *
 * @APPLE_OSREFERENCE_LICENSE_HEADER_END@
 */

/*	$NetBSD: tree.h,v 1.13 2006/08/27 22:32:38 christos Exp $	*/
/*	$OpenBSD: tree.h,v 1.7 2002/10/17 21:51:54 art Exp $	*/
/*
 * Copyright 2002 Niels Provos <provos@citi.umich.edu>
 * All rights reserved.
 *
 * Redistribution and use in source and binary forms, with or without
 * modification, are permitted provided that the following conditions
 * are met:
 * 1. Redistributions of source code must retain the above copyright
 *    notice, this list of conditions and the following disclaimer.
 * 2. Redistributions in binary form must reproduce the above copyright
 *    notice, this list of conditions and the following disclaimer in the
 *    documentation and/or other materials provided with the distribution.
 *
 * THIS SOFTWARE IS PROVIDED BY THE AUTHOR ``AS IS'' AND ANY EXPRESS OR
 * IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES
 * OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED.
 * IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR ANY DIRECT, INDIRECT,
 * INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT
 * NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,
 * DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
 * THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
 * (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF
 * THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
 */

#ifndef	_LIBKERN_TREE_H_
#define	_LIBKERN_TREE_H_

/*
 * This file defines data structures for different types of trees:
 * splay trees and red-black trees.
 *
 * A splay tree is a self-organizing data structure.  Every operation
 * on the tree causes a splay to happen.  The splay moves the requested
 * node to the root of the tree and partly rebalances it.
 *
 * This has the benefit that request locality causes faster lookups as
 * the requested nodes move to the top of the tree.  On the other hand,
 * every lookup causes memory writes.
 *
 * The Balance Theorem bounds the total access time for m operations
 * and n inserts on an initially empty tree as O((m + n)lg n).  The
 * amortized cost for a sequence of m accesses to a splay tree is O(lg n);
 *
 * A red-black tree is a binary search tree with the node color as an
 * extra attribute.  It fulfills a set of conditions:
 *	- every search path from the root to a leaf consists of the
 *	  same number of black nodes,
 *	- each red node (except for the root) has a black parent,
 *	- each leaf node is black.
 *
 * Every operation on a red-black tree is bounded as O(lg n).
 * The maximum height of a red-black tree is 2lg (n+1).
 */

#define SPLAY_HEAD(name, type)						\
struct name {								\
	struct type *sph_root; /* root of the tree */			\
}

#define SPLAY_INITIALIZER(root)						\
	{ NULL }

#define SPLAY_INIT(root) do {						\
	(root)->sph_root = NULL;					\
} while (/*CONSTCOND*/ 0)

#define SPLAY_ENTRY(type)						\
struct {								\
	struct type *spe_left; /* left element */			\
	struct type *spe_right; /* right element */			\
}

#define SPLAY_LEFT(elm, field)		(elm)->field.spe_left
#define SPLAY_RIGHT(elm, field)		(elm)->field.spe_right
#define SPLAY_ROOT(head)		(head)->sph_root
#define SPLAY_EMPTY(head)		(SPLAY_ROOT(head) == NULL)

/* SPLAY_ROTATE_{LEFT,RIGHT} expect that tmp hold SPLAY_{RIGHT,LEFT} */
#define SPLAY_ROTATE_RIGHT(head, tmp, field) do {			\
	SPLAY_LEFT((head)->sph_root, field) = SPLAY_RIGHT(tmp, field);	\
	SPLAY_RIGHT(tmp, field) = (head)->sph_root;			\
	(head)->sph_root = tmp;						\
} while (/*CONSTCOND*/ 0)

#define SPLAY_ROTATE_LEFT(head, tmp, field) do {			\
	SPLAY_RIGHT((head)->sph_root, field) = SPLAY_LEFT(tmp, field);	\
	SPLAY_LEFT(tmp, field) = (head)->sph_root;			\
	(head)->sph_root = tmp;						\
} while (/*CONSTCOND*/ 0)

#define SPLAY_LINKLEFT(head, tmp, field) do {				\
	SPLAY_LEFT(tmp, field) = (head)->sph_root;			\
	tmp = (head)->sph_root;						\
	(head)->sph_root = SPLAY_LEFT((head)->sph_root, field);		\
} while (/*CONSTCOND*/ 0)

#define SPLAY_LINKRIGHT(head, tmp, field) do {				\
	SPLAY_RIGHT(tmp, field) = (head)->sph_root;			\
	tmp = (head)->sph_root;						\
	(head)->sph_root = SPLAY_RIGHT((head)->sph_root, field);	\
} while (/*CONSTCOND*/ 0)

#define SPLAY_ASSEMBLE(head, node, left, right, field) do {		\
	SPLAY_RIGHT(left, field) = SPLAY_LEFT((head)->sph_root, field);	\
	SPLAY_LEFT(right, field) = SPLAY_RIGHT((head)->sph_root, field);\
	SPLAY_LEFT((head)->sph_root, field) = SPLAY_RIGHT(node, field);	\
	SPLAY_RIGHT((head)->sph_root, field) = SPLAY_LEFT(node, field);	\
} while (/*CONSTCOND*/ 0)

/* Generates prototypes and inline functions */

#define SPLAY_PROTOTYPE(name, type, field, cmp)				\
void name##_SPLAY(struct name *, struct type *);			\
void name##_SPLAY_MINMAX(struct name *, int);				\
struct type *name##_SPLAY_INSERT(struct name *, struct type *);		\
struct type *name##_SPLAY_REMOVE(struct name *, struct type *);		\
									\
/* Finds the node with the same key as elm */				\
static __inline struct type *						\
name##_SPLAY_FIND(struct name *head, struct type *elm)			\
{									\
	if (SPLAY_EMPTY(head))						\
		return(NULL);						\
	name##_SPLAY(head, elm);					\
	if ((cmp)(elm, (head)->sph_root) == 0)				\
		return (head->sph_root);				\
	return (NULL);							\
}									\
									\
static __inline struct type *						\
name##_SPLAY_NEXT(struct name *head, struct type *elm)			\
{									\
	name##_SPLAY(head, elm);					\
	if (SPLAY_RIGHT(elm, field) != NULL) {				\
		elm = SPLAY_RIGHT(elm, field);				\
		while (SPLAY_LEFT(elm, field) != NULL) {		\
			elm = SPLAY_LEFT(elm, field);			\
		}							\
	} else								\
		elm = NULL;						\
	return (elm);							\
}									\
									\
static __inline struct type *						\
name##_SPLAY_MIN_MAX(struct name *head, int val)			\
{									\
	name##_SPLAY_MINMAX(head, val);					\
        return (SPLAY_ROOT(head));					\
}

/* Main splay operation.
 * Moves node close to the key of elm to top
 */
#define SPLAY_GENERATE(name, type, field, cmp)				\
struct type *								\
name##_SPLAY_INSERT(struct name *head, struct type *elm)		\
{									\
    if (SPLAY_EMPTY(head)) {						\
	    SPLAY_LEFT(elm, field) = SPLAY_RIGHT(elm, field) = NULL;	\
    } else {								\
	    int __comp;							\
	    name##_SPLAY(head, elm);					\
	    __comp = (cmp)(elm, (head)->sph_root);			\
	    if(__comp < 0) {						\
		    SPLAY_LEFT(elm, field) = SPLAY_LEFT((head)->sph_root, field);\
		    SPLAY_RIGHT(elm, field) = (head)->sph_root;		\
		    SPLAY_LEFT((head)->sph_root, field) = NULL;		\
	    } else if (__comp > 0) {					\
		    SPLAY_RIGHT(elm, field) = SPLAY_RIGHT((head)->sph_root, field);\
		    SPLAY_LEFT(elm, field) = (head)->sph_root;		\
		    SPLAY_RIGHT((head)->sph_root, field) = NULL;	\
	    } else							\
		    return ((head)->sph_root);				\
    }									\
    (head)->sph_root = (elm);						\
    return (NULL);							\
}									\
									\
struct type *								\
name##_SPLAY_REMOVE(struct name *head, struct type *elm)		\
{									\
	struct type *__tmp;						\
	if (SPLAY_EMPTY(head))						\
		return (NULL);						\
	name##_SPLAY(head, elm);					\
	if ((cmp)(elm, (head)->sph_root) == 0) {			\
		if (SPLAY_LEFT((head)->sph_root, field) == NULL) {	\
			(head)->sph_root = SPLAY_RIGHT((head)->sph_root, field);\
		} else {						\
			__tmp = SPLAY_RIGHT((head)->sph_root, field);	\
			(head)->sph_root = SPLAY_LEFT((head)->sph_root, field);\
			name##_SPLAY(head, elm);			\
			SPLAY_RIGHT((head)->sph_root, field) = __tmp;	\
		}							\
		return (elm);						\
	}								\
	return (NULL);							\
}									\
									\
void									\
name##_SPLAY(struct name *head, struct type *elm)			\
{									\
	struct type __node, *__left, *__right, *__tmp;			\
	int __comp;							\
\
	SPLAY_LEFT(&__node, field) = SPLAY_RIGHT(&__node, field) = NULL;\
	__left = __right = &__node;					\
\
	while ((__comp = (cmp)(elm, (head)->sph_root)) != 0) {		\
		if (__comp < 0) {					\
			__tmp = SPLAY_LEFT((head)->sph_root, field);	\
			if (__tmp == NULL)				\
				break;					\
			if ((cmp)(elm, __tmp) < 0){			\
				SPLAY_ROTATE_RIGHT(head, __tmp, field);	\
				if (SPLAY_LEFT((head)->sph_root, field) == NULL)\
					break;				\
			}						\
			SPLAY_LINKLEFT(head, __right, field);		\
		} else if (__comp > 0) {				\
			__tmp = SPLAY_RIGHT((head)->sph_root, field);	\
			if (__tmp == NULL)				\
				break;					\
			if ((cmp)(elm, __tmp) > 0){			\
				SPLAY_ROTATE_LEFT(head, __tmp, field);	\
				if (SPLAY_RIGHT((head)->sph_root, field) == NULL)\
					break;				\
			}						\
			SPLAY_LINKRIGHT(head, __left, field);		\
		}							\
	}								\
	SPLAY_ASSEMBLE(head, &__node, __left, __right, field);		\
}									\
									\
/* Splay with either the minimum or the maximum element			\
 * Used to find minimum or maximum element in tree.			\
 */									\
void name##_SPLAY_MINMAX(struct name *head, int __comp) \
{									\
	struct type __node, *__left, *__right, *__tmp;			\
\
	SPLAY_LEFT(&__node, field) = SPLAY_RIGHT(&__node, field) = NULL;\
	__left = __right = &__node;					\
\
	while (1) {							\
		if (__comp < 0) {					\
			__tmp = SPLAY_LEFT((head)->sph_root, field);	\
			if (__tmp == NULL)				\
				break;					\
			if (__comp < 0){				\
				SPLAY_ROTATE_RIGHT(head, __tmp, field);	\
				if (SPLAY_LEFT((head)->sph_root, field) == NULL)\
					break;				\
			}						\
			SPLAY_LINKLEFT(head, __right, field);		\
		} else if (__comp > 0) {				\
			__tmp = SPLAY_RIGHT((head)->sph_root, field);	\
			if (__tmp == NULL)				\
				break;					\
			if (__comp > 0) {				\
				SPLAY_ROTATE_LEFT(head, __tmp, field);	\
				if (SPLAY_RIGHT((head)->sph_root, field) == NULL)\
					break;				\
			}						\
			SPLAY_LINKRIGHT(head, __left, field);		\
		}							\
	}								\
	SPLAY_ASSEMBLE(head, &__node, __left, __right, field);		\
}

#define SPLAY_NEGINF	-1
#define SPLAY_INF	1

#define SPLAY_INSERT(name, x, y)	name##_SPLAY_INSERT(x, y)
#define SPLAY_REMOVE(name, x, y)	name##_SPLAY_REMOVE(x, y)
#define SPLAY_FIND(name, x, y)		name##_SPLAY_FIND(x, y)
#define SPLAY_NEXT(name, x, y)		name##_SPLAY_NEXT(x, y)
#define SPLAY_MIN(name, x)		(SPLAY_EMPTY(x) ? NULL	\
					: name##_SPLAY_MIN_MAX(x, SPLAY_NEGINF))
#define SPLAY_MAX(name, x)		(SPLAY_EMPTY(x) ? NULL	\
					: name##_SPLAY_MIN_MAX(x, SPLAY_INF))

#define SPLAY_FOREACH(x, name, head)					\
	for ((x) = SPLAY_MIN(name, head);				\
	     (x) != NULL;						\
	     (x) = SPLAY_NEXT(name, head, x))

/* Macros that define a red-black tree */
#define RB_HEAD(name, type)						\
struct name {								\
	struct type *rbh_root; /* root of the tree */			\
}

#define RB_INITIALIZER(root)						\
	{ NULL }

#define RB_INIT(root) do {						\
	(root)->rbh_root = NULL;					\
} while (/*CONSTCOND*/ 0)

#define RB_BLACK	0
#define RB_RED		1
#define RB_PLACEHOLDER	NULL
#define RB_ENTRY(type)							\
struct {								\
	struct type *rbe_left;		/* left element */		\
	struct type *rbe_right;		/* right element */		\
	struct type *rbe_parent;	/* parent element */		\
}

#define RB_COLOR_MASK			(uintptr_t)0x1
#define RB_LEFT(elm, field)		(elm)->field.rbe_left
#define RB_RIGHT(elm, field)		(elm)->field.rbe_right
#define _RB_PARENT(elm, field)		(elm)->field.rbe_parent
#define RB_ROOT(head)			(head)->rbh_root
#define RB_EMPTY(head)			(RB_ROOT(head) == NULL)

#define RB_SET(name, elm, parent, field) do {					\
	name##_RB_SETPARENT(elm, parent);					\
	RB_LEFT(elm, field) = RB_RIGHT(elm, field) = NULL;		\
	name##_RB_SETCOLOR(elm, RB_RED);				\
} while (/*CONSTCOND*/ 0)

#define RB_SET_BLACKRED(name, black, red, field) do {				\
	name##_RB_SETCOLOR(black,  RB_BLACK);				\
	name##_RB_SETCOLOR(red, RB_RED);					\
} while (/*CONSTCOND*/ 0)

#ifndef RB_AUGMENT
#define RB_AUGMENT(x) (void)(x)
#endif

#define RB_ROTATE_LEFT(name, head, elm, tmp, field) do {			\
	(tmp) = RB_RIGHT(elm, field);					\
	if ((RB_RIGHT(elm, field) = RB_LEFT(tmp, field)) != NULL) {	\
		name##_RB_SETPARENT(RB_LEFT(tmp, field),(elm));		\
	}								\
	RB_AUGMENT(elm);						\
	if (name##_RB_SETPARENT(tmp, name##_RB_GETPARENT(elm)) != NULL) {	\
		if ((elm) == RB_LEFT(name##_RB_GETPARENT(elm), field))	\
			RB_LEFT(name##_RB_GETPARENT(elm), field) = (tmp);	\
		else							\
			RB_RIGHT(name##_RB_GETPARENT(elm), field) = (tmp);	\
	} else								\
		(head)->rbh_root = (tmp);				\
	RB_LEFT(tmp, field) = (elm);					\
	name##_RB_SETPARENT(elm, (tmp));					\
	RB_AUGMENT(tmp);						\
	if ((name##_RB_GETPARENT(tmp)))					\
		RB_AUGMENT(name##_RB_GETPARENT(tmp));			\
} while (/*CONSTCOND*/ 0)

#define RB_ROTATE_RIGHT(name, head, elm, tmp, field) do {			\
	(tmp) = RB_LEFT(elm, field);					\
	if ((RB_LEFT(elm, field) = RB_RIGHT(tmp, field)) != NULL) {	\
		name##_RB_SETPARENT(RB_RIGHT(tmp, field), (elm));		\
	}								\
	RB_AUGMENT(elm);						\
	if (name##_RB_SETPARENT(tmp, name##_RB_GETPARENT(elm)) != NULL) {	\
		if ((elm) == RB_LEFT(name##_RB_GETPARENT(elm), field))	\
			RB_LEFT(name##_RB_GETPARENT(elm), field) = (tmp);	\
		else							\
			RB_RIGHT(name##_RB_GETPARENT(elm), field) = (tmp);	\
	} else								\
		(head)->rbh_root = (tmp);				\
	RB_RIGHT(tmp, field) = (elm);					\
	name##_RB_SETPARENT(elm, tmp);					\
	RB_AUGMENT(tmp);						\
	if ((name##_RB_GETPARENT(tmp)))					\
		RB_AUGMENT(name##_RB_GETPARENT(tmp));			\
} while (/*CONSTCOND*/ 0)

/* Generates prototypes and inline functions */
#define RB_PROTOTYPE(name, type, field, cmp)				\
void name##_RB_INSERT_COLOR(struct name *, struct type *);	\
void name##_RB_REMOVE_COLOR(struct name *, struct type *, struct type *);\
struct type *name##_RB_REMOVE(struct name *, struct type *);		\
struct type *name##_RB_INSERT(struct name *, struct type *);		\
struct type *name##_RB_FIND(struct name *, struct type *);		\
struct type *name##_RB_NEXT(struct type *);				\
struct type *name##_RB_MINMAX(struct name *, int);			\
struct type *name##_RB_GETPARENT(struct type*);				\
struct type *name##_RB_SETPARENT(struct type*, struct type*);		\
int name##_RB_GETCOLOR(struct type*);					\
void name##_RB_SETCOLOR(struct type*,int);				

/* Generates prototypes (with storage class) and inline functions */
#define RB_PROTOTYPE_SC(_sc_, name, type, field, cmp)			\
_sc_ void name##_RB_INSERT_COLOR(struct name *, struct type *);		\
_sc_ void name##_RB_REMOVE_COLOR(struct name *, struct type *, struct type *); \
_sc_ struct type *name##_RB_REMOVE(struct name *, struct type *);	\
_sc_ struct type *name##_RB_INSERT(struct name *, struct type *);	\
_sc_ struct type *name##_RB_FIND(struct name *, struct type *);		\
_sc_ struct type *name##_RB_NEXT(struct type *);			\
_sc_ struct type *name##_RB_MINMAX(struct name *, int);			\
_sc_ struct type *name##_RB_GETPARENT(struct type*);			\
_sc_ struct type *name##_RB_SETPARENT(struct type*, struct type*);			\
_sc_ int name##_RB_GETCOLOR(struct type*);			\
_sc_ void name##_RB_SETCOLOR(struct type*,int);


/* Main rb operation.
 * Moves node close to the key of elm to top
 */
#define RB_GENERATE(name, type, field, cmp)				\
struct type *name##_RB_GETPARENT(struct type *elm) {				\
	struct type *parent = _RB_PARENT(elm, field);			\
	if( parent != NULL) {						\
		parent = (struct type*)((uintptr_t)parent & ~RB_COLOR_MASK);\
		return( (struct type*) ( (parent == (struct type*) RB_PLACEHOLDER) ? NULL: parent));\
	}								\
	return((struct type*)NULL);					\
}									\
int name##_RB_GETCOLOR(struct type *elm) {					\
	int color = 0;							\
	color = (int)((uintptr_t)_RB_PARENT(elm,field) & RB_COLOR_MASK);\
	return(color);							\
}									\
void name##_RB_SETCOLOR(struct type *elm,int color) {				\
	struct type *parent = name##_RB_GETPARENT(elm);			\
	if(parent == (struct type*)NULL) 				\
		parent = (struct type*) RB_PLACEHOLDER;			\
	_RB_PARENT(elm, field) = (struct type*)((uintptr_t)parent | (unsigned int)color);\
}									\
struct type *name##_RB_SETPARENT(struct type *elm, struct type *parent) {	\
	int color = name##_RB_GETCOLOR(elm);					\
	_RB_PARENT(elm, field) = parent;				\
	if(color) name##_RB_SETCOLOR(elm, color);				\
	return(name##_RB_GETPARENT(elm));					\
}									\
									\
void									\
name##_RB_INSERT_COLOR(struct name *head, struct type *elm)		\
{									\
	struct type *parent, *gparent, *tmp;				\
	while ((parent = name##_RB_GETPARENT(elm)) != NULL &&		\
	    name##_RB_GETCOLOR(parent) == RB_RED) {			\
		gparent = name##_RB_GETPARENT(parent);			\
		if (parent == RB_LEFT(gparent, field)) {		\
			tmp = RB_RIGHT(gparent, field);			\
			if (tmp && name##_RB_GETCOLOR(tmp) == RB_RED) {	\
				name##_RB_SETCOLOR(tmp,  RB_BLACK);	\
				RB_SET_BLACKRED(name, parent, gparent, field);\
				elm = gparent;				\
				continue;				\
			}						\
			if (RB_RIGHT(parent, field) == elm) {		\
				RB_ROTATE_LEFT(name, head, parent, tmp, field);\
				tmp = parent;				\
				parent = elm;				\
				elm = tmp;				\
			}						\
			RB_SET_BLACKRED(name, parent, gparent, field);	\
			RB_ROTATE_RIGHT(name,head, gparent, tmp, field);	\
		} else {						\
			tmp = RB_LEFT(gparent, field);			\
			if (tmp && name##_RB_GETCOLOR(tmp) == RB_RED) {	\
				name##_RB_SETCOLOR(tmp,  RB_BLACK);	\
				RB_SET_BLACKRED(name, parent, gparent, field);\
				elm = gparent;				\
				continue;				\
			}						\
			if (RB_LEFT(parent, field) == elm) {		\
				RB_ROTATE_RIGHT(name, head, parent, tmp, field);\
				tmp = parent;				\
				parent = elm;				\
				elm = tmp;				\
			}						\
			RB_SET_BLACKRED(name, parent, gparent, field);	\
			RB_ROTATE_LEFT(name, head, gparent, tmp, field);	\
		}							\
	}								\
	name##_RB_SETCOLOR(head->rbh_root,  RB_BLACK);			\
}									\
									\
void									\
name##_RB_REMOVE_COLOR(struct name *head, struct type *parent, struct type *elm) \
{									\
	struct type *tmp;						\
	while ((elm == NULL || name##_RB_GETCOLOR(elm) == RB_BLACK) &&	\
	    elm != RB_ROOT(head)) {					\
		if (RB_LEFT(parent, field) == elm) {			\
			tmp = RB_RIGHT(parent, field);			\
			if (name##_RB_GETCOLOR(tmp) == RB_RED) {		\
				RB_SET_BLACKRED(name, tmp, parent, field);	\
				RB_ROTATE_LEFT(name, head, parent, tmp, field);\
				tmp = RB_RIGHT(parent, field);		\
			}						\
			if ((RB_LEFT(tmp, field) == NULL ||		\
			    name##_RB_GETCOLOR(RB_LEFT(tmp, field)) == RB_BLACK) &&\
			    (RB_RIGHT(tmp, field) == NULL ||		\
			    name##_RB_GETCOLOR(RB_RIGHT(tmp, field)) == RB_BLACK)) {\
				name##_RB_SETCOLOR(tmp,  RB_RED);		\
				elm = parent;				\
				parent = name##_RB_GETPARENT(elm);		\
			} else {					\
				if (RB_RIGHT(tmp, field) == NULL ||	\
				    name##_RB_GETCOLOR(RB_RIGHT(tmp, field)) == RB_BLACK) {\
					struct type *oleft;		\
					if ((oleft = RB_LEFT(tmp, field)) \
					    != NULL)			\
						name##_RB_SETCOLOR(oleft,  RB_BLACK);\
					name##_RB_SETCOLOR(tmp, RB_RED);	\
					RB_ROTATE_RIGHT(name, head, tmp, oleft, field);\
					tmp = RB_RIGHT(parent, field);	\
				}					\
				name##_RB_SETCOLOR(tmp, (name##_RB_GETCOLOR(parent)));\
				name##_RB_SETCOLOR(parent, RB_BLACK);	\
				if (RB_RIGHT(tmp, field))		\
					name##_RB_SETCOLOR(RB_RIGHT(tmp, field),RB_BLACK);\
				RB_ROTATE_LEFT(name, head, parent, tmp, field);\
				elm = RB_ROOT(head);			\
				break;					\
			}						\
		} else {						\
			tmp = RB_LEFT(parent, field);			\
			if (name##_RB_GETCOLOR(tmp) == RB_RED) {		\
				RB_SET_BLACKRED(name, tmp, parent, field);	\
				RB_ROTATE_RIGHT(name, head, parent, tmp, field);\
				tmp = RB_LEFT(parent, field);		\
			}						\
			if ((RB_LEFT(tmp, field) == NULL ||		\
			    name##_RB_GETCOLOR(RB_LEFT(tmp, field)) == RB_BLACK) &&\
			    (RB_RIGHT(tmp, field) == NULL ||		\
			    name##_RB_GETCOLOR(RB_RIGHT(tmp, field)) == RB_BLACK)) {\
				name##_RB_SETCOLOR(tmp, RB_RED);		\
				elm = parent;				\
				parent = name##_RB_GETPARENT(elm);		\
			} else {					\
				if (RB_LEFT(tmp, field) == NULL ||	\
				    name##_RB_GETCOLOR(RB_LEFT(tmp, field)) == RB_BLACK) {\
					struct type *oright;		\
					if ((oright = RB_RIGHT(tmp, field)) \
					    != NULL)			\
						name##_RB_SETCOLOR(oright,  RB_BLACK);\
					name##_RB_SETCOLOR(tmp,  RB_RED);	\
					RB_ROTATE_LEFT(name, head, tmp, oright, field);\
					tmp = RB_LEFT(parent, field);	\
				}					\
				name##_RB_SETCOLOR(tmp,(name##_RB_GETCOLOR(parent)));\
				name##_RB_SETCOLOR(parent, RB_BLACK);	\
				if (RB_LEFT(tmp, field))		\
					name##_RB_SETCOLOR(RB_LEFT(tmp, field), RB_BLACK);\
				RB_ROTATE_RIGHT(name, head, parent, tmp, field);\
				elm = RB_ROOT(head);			\
				break;					\
			}						\
		}							\
	}								\
	if (elm)							\
		name##_RB_SETCOLOR(elm,  RB_BLACK);			\
}									\
									\
struct type *								\
name##_RB_REMOVE(struct name *head, struct type *elm)			\
{									\
	struct type *child, *parent, *old = elm;			\
	int color;							\
	if (RB_LEFT(elm, field) == NULL)				\
		child = RB_RIGHT(elm, field);				\
	else if (RB_RIGHT(elm, field) == NULL)				\
		child = RB_LEFT(elm, field);				\
	else {								\
		struct type *left;					\
		elm = RB_RIGHT(elm, field);				\
		while ((left = RB_LEFT(elm, field)) != NULL)		\
			elm = left;					\
		child = RB_RIGHT(elm, field);				\
		parent = name##_RB_GETPARENT(elm);				\
		color = name##_RB_GETCOLOR(elm);				\
		if (child)						\
			name##_RB_SETPARENT(child, parent);		\
		if (parent) {						\
			if (RB_LEFT(parent, field) == elm)		\
				RB_LEFT(parent, field) = child;		\
			else						\
				RB_RIGHT(parent, field) = child;	\
			RB_AUGMENT(parent);				\
		} else							\
			RB_ROOT(head) = child;				\
		if (name##_RB_GETPARENT(elm) == old)			\
			parent = elm;					\
		(elm)->field = (old)->field;				\
		if (name##_RB_GETPARENT(old)) {				\
			if (RB_LEFT(name##_RB_GETPARENT(old), field) == old)\
				RB_LEFT(name##_RB_GETPARENT(old), field) = elm;\
			else						\
				RB_RIGHT(name##_RB_GETPARENT(old), field) = elm;\
			RB_AUGMENT(name##_RB_GETPARENT(old));		\
		} else							\
			RB_ROOT(head) = elm;				\
		name##_RB_SETPARENT(RB_LEFT(old, field), elm);		\
		if (RB_RIGHT(old, field))				\
			name##_RB_SETPARENT(RB_RIGHT(old, field), elm);	\
		if (parent) {						\
			left = parent;					\
			do {						\
				RB_AUGMENT(left);			\
			} while ((left = name##_RB_GETPARENT(left)) != NULL); \
		}							\
		goto color;						\
	}								\
	parent = name##_RB_GETPARENT(elm);					\
	color = name##_RB_GETCOLOR(elm);					\
	if (child)							\
		name##_RB_SETPARENT(child, parent);			\
	if (parent) {							\
		if (RB_LEFT(parent, field) == elm)			\
			RB_LEFT(parent, field) = child;			\
		else							\
			RB_RIGHT(parent, field) = child;		\
		RB_AUGMENT(parent);					\
	} else								\
		RB_ROOT(head) = child;					\
color:									\
	if (color == RB_BLACK)						\
		name##_RB_REMOVE_COLOR(head, parent, child);		\
	return (old);							\
}									\
									\
/* Inserts a node into the RB tree */					\
struct type *								\
name##_RB_INSERT(struct name *head, struct type *elm)			\
{									\
	struct type *tmp;						\
	struct type *parent = NULL;					\
	int comp = 0;							\
	tmp = RB_ROOT(head);						\
	while (tmp) {							\
		parent = tmp;						\
		comp = (cmp)(elm, parent);				\
		if (comp < 0)						\
			tmp = RB_LEFT(tmp, field);			\
		else if (comp > 0)					\
			tmp = RB_RIGHT(tmp, field);			\
		else							\
			return (tmp);					\
	}								\
	RB_SET(name, elm, parent, field);					\
	if (parent != NULL) {						\
		if (comp < 0)						\
			RB_LEFT(parent, field) = elm;			\
		else							\
			RB_RIGHT(parent, field) = elm;			\
		RB_AUGMENT(parent);					\
	} else								\
		RB_ROOT(head) = elm;					\
	name##_RB_INSERT_COLOR(head, elm);				\
	return (NULL);							\
}									\
									\
/* Finds the node with the same key as elm */				\
struct type *								\
name##_RB_FIND(struct name *head, struct type *elm)			\
{									\
	struct type *tmp = RB_ROOT(head);				\
	int comp;							\
	while (tmp) {							\
		comp = cmp(elm, tmp);					\
		if (comp < 0)						\
			tmp = RB_LEFT(tmp, field);			\
		else if (comp > 0)					\
			tmp = RB_RIGHT(tmp, field);			\
		else							\
			return (tmp);					\
	}								\
	return (NULL);							\
}									\
									\
/* ARGSUSED */								\
struct type *								\
name##_RB_NEXT(struct type *elm)					\
{									\
	if (RB_RIGHT(elm, field)) {					\
		elm = RB_RIGHT(elm, field);				\
		while (RB_LEFT(elm, field))				\
			elm = RB_LEFT(elm, field);			\
	} else {							\
		if (name##_RB_GETPARENT(elm) &&				\
		    (elm == RB_LEFT(name##_RB_GETPARENT(elm), field)))	\
			elm = name##_RB_GETPARENT(elm);			\
		else {							\
			while (name##_RB_GETPARENT(elm) &&			\
			    (elm == RB_RIGHT(name##_RB_GETPARENT(elm), field)))\
				elm = name##_RB_GETPARENT(elm);		\
			elm = name##_RB_GETPARENT(elm);			\
		}							\
	}								\
	return (elm);							\
}									\
									\
struct type *								\
name##_RB_MINMAX(struct name *head, int val)				\
{									\
	struct type *tmp = RB_ROOT(head);				\
	struct type *parent = NULL;					\
	while (tmp) {							\
		parent = tmp;						\
		if (val < 0)						\
			tmp = RB_LEFT(tmp, field);			\
		else							\
			tmp = RB_RIGHT(tmp, field);			\
	}								\
	return (parent);						\
}


#define RB_PROTOTYPE_PREV(name, type, field, cmp)			\
	RB_PROTOTYPE(name, type, field, cmp)				\
struct type *name##_RB_PREV(struct type *);


#define RB_PROTOTYPE_SC_PREV(_sc_, name, type, field, cmp)		\
	RB_PROTOTYPE_SC(_sc_, name, type, field, cmp)			\
_sc_ struct type *name##_RB_PREV(struct type *);

#define RB_GENERATE_PREV(name, type, field, cmp)			\
	RB_GENERATE(name, type, field, cmp)				\
struct type *								\
name##_RB_PREV(struct type *elm)					\
{									\
	if (RB_LEFT(elm, field)) {					\
		elm = RB_LEFT(elm, field);				\
		while (RB_RIGHT(elm, field))				\
			elm = RB_RIGHT(elm, field);			\
	} else {							\
		if (name##_RB_GETPARENT(elm) &&				\
		    (elm == RB_RIGHT(name##_RB_GETPARENT(elm), field)))	\
			elm = name##_RB_GETPARENT(elm);			\
		else {							\
			while (name##_RB_GETPARENT(elm) &&		\
			    (elm == RB_LEFT(name##_RB_GETPARENT(elm), field)))\
				elm = name##_RB_GETPARENT(elm);		\
			elm = name##_RB_GETPARENT(elm);			\
		}							\
	}								\
	return (elm);							\
}									\

#define RB_NEGINF	-1
#define RB_INF	1

#define RB_INSERT(name, x, y)	name##_RB_INSERT(x, y)
#define RB_REMOVE(name, x, y)	name##_RB_REMOVE(x, y)
#define RB_FIND(name, x, y)	name##_RB_FIND(x, y)
#define RB_NEXT(name, x, y)	name##_RB_NEXT(y)
#define RB_PREV(name, x, y)	name##_RB_PREV(y)
#define RB_MIN(name, x)		name##_RB_MINMAX(x, RB_NEGINF)
#define RB_MAX(name, x)		name##_RB_MINMAX(x, RB_INF)

#define RB_FOREACH(x, name, head)					\
	for ((x) = RB_MIN(name, head);					\
	     (x) != NULL;						\
	     (x) = name##_RB_NEXT(x))

#define RB_FOREACH_FROM(x, name, y)                                     \
	for ((x) = (y);                                                 \
	    ((x) != NULL) && ((y) = name##_RB_NEXT(x), (x) != NULL);    \
            (x) = (y))

#define RB_FOREACH_REVERSE_FROM(x, name, y)				\
	for ((x) = (y);							\
	    ((x) != NULL) && ((y) = name##_RB_PREV(x), (x) != NULL);	\
	     (x) = (y))

#define RB_FOREACH_SAFE(x, name, head, y)				\
	for ((x) = RB_MIN(name, head);					\
	    ((x) != NULL) && ((y) = name##_RB_NEXT(x), (x) != NULL);	\
	     (x) = (y))

#endif	/* _LIBKERN_TREE_H_ */